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arXiv · 2507.00213

The Hamiltonian surface of $\Aut(F_2)$

Sylvain Barré·Mikaël Pichot
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Abstract

The group of automorphisms of the free group on two generators is known to act geometrically, in an essentially unique way, on a 2-dimensional CAT(0) space X. We prove that X contains precisely two Hamiltonian surfaces. By this we mean a surface in X which visits every vertex and every edge precisely once.

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Sylvain Barré, Mikaël Pichot. 2025-06-30. The Hamiltonian surface of $\Aut(F_2)$. https://arxiv.org/abs/2507.00213

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